The conversion of signals from an analog format to a digitized format and back to an analog format has been known for many years. Typical applications wherein digital-to-analog (D/A) and analog-to-digital (A/D) signal conversion equipment is used include telephone systems, audio/visual systems, television systems, other telecommunication systems, and many other varied applications requiring the conversion of signals from one format to another.
In many situations, in the transmission of analog signals, it is advantageous to digitize the analog signal, transmit the digitized analog signal over a communications link, receive the digitized analog signal, convert the digitized analog signal to an analog signal, and convey the analog signal. For example, in digital telephone systems, an analog signal is generated by a local user, digitized using a coder/decoder (CODEC) into a digitized analog signal, transmitted in a digitized format to a receiving location over a digitized link, transformed from the digitized format back into an analog format at the receiving location with another CODEC, and provided to the remote user in an analog format. The conversion of analog signals to a digital representation enables the use of digital processing elements for manipulation of the signal.
As is the case with any telecommunications environment, a telephone system defines a frequency bandwidth for its operation. In many phone systems, the frequency bandwidth is 0 to 4 kHz which provides sufficient bandwidth for the usual conversations transmitted across the telephone link.
At a transmitting location, a CODEC or other converter converts an analog signal received from the user into a digitized analog signal. The bandwidth of interest extends only to 4 kHz, and preserving all of the information up to 4 kHz requires sampling the signal at the Nyquist rate of 8 kHz, which is twice the maximum frequency of interest. In standard telephone systems, the signal sampled at a sampling rate of 8 kHz is represented by 13 bits of binary data at each sampling interval, the 13 bits representing the magnitude of each digitized analog signal sample. The digitized analog signal is then transmitted across a digital link and received by a receiving CODEC.
The conversion of signals from a digitized format to an analog format is difficult to perform when a large number of bits, such as 13, represents the value of each sample. This difficulty is greatly reduced as the number of bits used to represent the signal for conversion is reduced. Oversampling Converters have been developed to make use of the fact that a trade-off exists between the sampling frequency of a digitized signal and the number of bits required to represent it. When a higher sampling frequency is used to digitize an analog signal, fewer bits are required to accurately preserve the information.
A technique known as "noise shaping" increases the performance of oversampling converters by modifying the frequency response of the quantization noise introduced when the number of bits used to represent a signal is reduced by increasing the sampling rate. By using noise shaping, the quantization noise in the frequency band of interest (i.e., 0 to 4 kHz in telephone systems) is reduced, while the quantization noise at frequencies close to the sampling frequency increases. Thus, oversampling converters which employ noise shaping allow for the reduction in the number of bits needed to represent a signal. In some applications, this type of system will allow the number of bits required per sample to be reduced to a single bit.
In Oversampling Converters with Noise Shaping, the increase in the sampling frequency (known as interpolation) is usually carried out in two or more steps. This makes the elimination of frequency aliases (images of the signal of interest at multiples of the initial sampling frequency) more tractable. In a typical system, a small interpolation step is used to reach an intermediate sampling frequency, and a large interpolation step is used to reach the final sampling rate. In one example system, a first linear interpolator increases the sampling rate from 8 kHz to 32 kHz, a factor-of-four interpolation step. A linear interpolator increases the sampling rate by taking each sample at the initial sampling rate and repeating it, at the target sampling rate, the number of times equal to the interpolation step.
As is known in the art, the interpolation process introduces aliases at each multiple of the initial sampling frequency up to the intermediate frequency. Thus, in systems where the digitized signal has been interpolated from 8 kHz to 32 kHz, aliases of the analog signal are centered at 8 kHz, 16 kHz, 24 kHz, and 32 kHz. To remove the aliases, the digitized analog signal is passed through an anti-alias filter. Once the signal is alias filtered, it is interpolated again to a much higher frequency. In a common application, the digitized analog signal that is sampled at 32 kHz at an intermediate sampling rate is interpolated to a sampling frequency of 1 MHz, a factor-of-32 interpolation.
The removal of aliases introduced by this second interpolation presents a different problem due to the high frequency of the resulting signal. For example, the processing requirements of conventional base-band filters make their use impractical. A linear interpolator provides some alias removal around multiples of the intermediate frequency, but in some applications, the amount of removal may not be sufficient. A comb interpolator, or comb filter, provides superior performance for the removal of frequency aliases, but at the expense of additional hardware.
Once the digitized signal has been interpolated to a final sampling rate, it is then input to a noise shaper filter, which enables a reduction in the number of bits used to represent each sample. As mentioned before, this occurs at the expense of quantization noise that is introduced at frequencies that are outside the band of interest. For instance, in a sigma-delta noise shaper used in the digital-to-analog path in telephony applications, the frequency band from 0 to 4 kHz is not significantly affected by the quantization noise introduced by the noise shaper filter. Thus, the output of the noise shaper filter is a bit-reduced, high frequency, digitized analog signal that is provided to a digital-to-analog converter to produce an analog signal.
A major drawback of prior-art oversampling digital-to-analog converters was that the aliased signals introduced in the second interpolation step are difficult and expensive to remove with circuits known in the art. Furthermore, the less expensive option of linear interpolation provides inferior performance in the removal of such alias components. As stated, the alias signals contained in the digitized analog signal create noise in the analog signal and degrade the performance of the entire system in which they reside.
Thus, there is a need in the art for circuitry and a related methodology for removing aliased signals from a digitized analog signal in a digital-to-analog converter in a cost effective manner.